ACF329 Practice Problems for Final ExamWarning: this is not a sample test, and it only includes material not covered in the midterms.Name:Instructions: You should use one of the SOA approved calculators on this worksheet.These problems are from the sample Exam FM problems you can access from the Society of Actu-aries webpages. Some of them are slightly modified.Make sure you know how to use your calculator. I will not answer any questions during the exam onhow to use the calculator.For example, “BGN” versus “END”; although it’s possible to calculateall annuity symbols with just one of them, it may be more convenient to be able to use both.1.Important!This one item is not a problem, but a written correction of an error I madeduring class. One of the formulas from Section 3.9 (Annuities with payments in arithmeticprogression) was presented incorrectly. In class, I wrote (IP,Q¨a)∞i=P¨a∞i+Qd¨a∞i=Pd+Qd2.That was incorrect! The correct formula is(IP,Q¨a)∞i=P¨a∞i+Qda∞i=Pd+QidI apologize for any confusion I may have caused by this error. I have never used this formulato solve any problems in class so hopefully only a minor correction is needed in your notes.2. You are given the following information with respect to a bond:Par amount: 1000Term to maturity: 3 yearsannual coupon rate: 6% payable annuallyTermAnnual Spot Interest Rates17%28%39%Calculate the value of the bond and the annual effective yield rate for the bond if the bondis sold at a price equal to its value.ACF329 Spring 2011Harper

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3. A 1000 bond with semi-annual coupons ati(2)= 6% matures at par on October 15, 2020. Thebond is purchased on June 28, 2005 to yield the investori(2)= 7%. Calculate the purchaseprice to the nearest whole number. Assume simple interest between bond coupon dates. Also,assume that there are 183 days between coupon dates, and note that:DateDay of the YearApril 15105June 28179October 152884. The current price of an annual coupon bond is 100. The derivative of the price of the bondwith respect to the yield to maturity is-700. The yield to maturity is an annual effectiverate of 8%. Calculate the duration of the bond.5. Calculate the duration of a common stock that pays dividends at the end of each year intoperpetuity. Assume that the dividend is constant, and that the effective rate of interest is10%.6. Calculate the duration of a common stock that pays dividends at the end of each year intoperpetuity. Assume that the dividend increases by 2% each year and that the effective rateof interest is 5%.

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